3 papers
math.OC2026
Riemannian optimization framework on the generalized quaternionic Stiefel Manifold
Hiroyuki Sato
This paper introduces the generalized quaternionic Stiefel manifold and studies its geometry for Riemannian optimization. We clarify its relationships with existing manifolds, espe…
math.OC2026
Second-order geometry and Riemannian Newton-type methods for optimization on the indefinite Stiefel manifold
Hiroyuki Sato
This paper investigates the second-order geometry of the indefinite Stiefel manifold and derives explicit formulas for the Levi-Civita connection and the Riemannian Hessian under t…
math.OC2025
Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost
Hiroyuki Sato, Yuya Yamakawa, Kensuke Aihara
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the A…